I wasn't too sure how to add this to the page in a coherent manner so I'll add it here for the time being:
1: After the initial effect wears off the following message can occur after combat:
You feel lucky! Maybe the toad statue's still rubbing off on you.
You've gained 10 energy of Smiling Artist.
In my case it was a repeat of the initial effect but just what effect it chooses is unclear.
2: If the initial effect is still active the following message can occur following combat:
You feel lucky today! It's gotta be the toad!
This makes it possible to run the toad's stomach again.
3: Once the toad is ready again it behaves as normal if you rub it with no effect active. In the event you rub it with a Smiling effect active you receive the following:
You rub the toad's stomach asking for different luck. You're not sure if it's the toad or you, but you're feeling a bit different… maybe even lucky.
You've gained <X> energy of <Smiling Effect>.
The statue sits near your front door, staring at you passively.
Where <X> is equal to your current effect duration +10 and the effect appears to be a randomly selected different Smiling effect.
Gone fishin', be back at dark-thirty!